Question: Solve for $q$, $ -\dfrac{5}{4q - 2} = \dfrac{7}{4q - 2} + \dfrac{q + 1}{20q - 10} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $4q - 2$ $4q - 2$ and $20q - 10$ The common denominator is $20q - 10$ To get $20q - 10$ in the denominator of the first term, multiply it by $\frac{5}{5}$ $ -\dfrac{5}{4q - 2} \times \dfrac{5}{5} = -\dfrac{25}{20q - 10} $ To get $20q - 10$ in the denominator of the second term, multiply it by $\frac{5}{5}$ $ \dfrac{7}{4q - 2} \times \dfrac{5}{5} = \dfrac{35}{20q - 10} $ The denominator of the third term is already $20q - 10$ , so we don't need to change it. This give us: $ -\dfrac{25}{20q - 10} = \dfrac{35}{20q - 10} + \dfrac{q + 1}{20q - 10} $ If we multiply both sides of the equation by $20q - 10$ , we get: $ -25 = 35 + q + 1$ $ -25 = q + 36$ $ -61 = q $ $ q = -61$